I need help understanding the following condition:
$u_h\in L^2(\mathbb{T}^d)$, $\|u_h\|_{L^2(\mathbb{T}^d)}=1$, where $h$ is the semiclassical parameter and $\mathbb{T}^d$ is the flat torus, is called $h$-oscillating if
$\limsup_{h\rightarrow0^+}\|1_{[0,R]}(h^2\Delta) u_h\|_{L^2(\mathbb{T}^d)}\underset{R\rightarrow\infty}{\longrightarrow}0$
Any examples, counterexamples, help are appreciated. Thanks!
